PHYSICAL REVIEW A 67, 053406 共2003兲
Magneto-optical trap for metastable helium at 389 nm
J. C. J. Koelemeij,* R. J. W. Stas, W. Hogervorst, and W. Vassen
Laser Centre Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
共Received 16 October 2002; published 29 May 2003兲
We have constructed a magneto-optical trap 共MOT兲 for metastable triplet helium atoms utilizing the 2 3 S 1
→3 3 P 2 line at 389 nm as the trapping and cooling transition. The far-red-detuned MOT 共detuning ⌬⫽
⫺41 MHz) typically contains few times 107 atoms at a relatively high (⬃109 cm⫺3 ) density, which is a
consequence of the large momentum transfer per photon at 389 nm and a small two-body loss rate coefficient
(2⫻10⫺10 cm3 /s⬍ ␤ ⬍1.0⫻10⫺9 cm3 /s). The two-body loss rate is more than five times smaller than in a
MOT on the commonly used 2 3 S 1 →2 3 P 2 line at 1083 nm. Furthermore, laser cooling at 389 nm results in
temperatures somewhat lower than those achieved using 1083 nm. The 389-nm MOT exhibits small losses due
to two-photon ionization, which have been investigated as well.
DOI: 10.1103/PhysRevA.67.053406
PACS number共s兲: 32.80.Pj, 34.50.Fa, 34.50.Rk
I. INTRODUCTION
A magneto-optical trap 共MOT兲 is a standard tool in the
production of cold atomic gases, allowing investigation of
cold-collision phenomena 关1兴 as well as the realization of
Bose-Einstein condensation 共BEC兲 in alkali-metal species
关2兴 and, more recently, in metastable triplet helium 共He*兲
关3,4兴. He* has a high 共19.8 eV兲 internal energy, which allows
for real-time diagnostics and increased sensitivity in BEC
probing. Unfortunately, the high internal energy also introduces strong Penning ionization losses in magneto-optically
trapped atomic clouds, which imposes limits on the maximum achievable density. The two-body loss rate coefficient
related to this process is about 5⫻10⫺9 cm3 /s for a MOT on
the 2 3 S 1 →2 3 P 2 transition at 1083 nm 关5兴, which is about
two orders of magnitude larger than the loss rate coefficient
in a standard alkali-metal MOT. In BEC experiments, a MOT
is used as a bright source of cold atoms to load a magnetic
trap with large numbers of atoms. Moreover, as a starting
point for evaporative cooling, a dense magnetostatically
trapped cloud is desired. So ideally, the magneto-optically
trapped cloud must provide this high density. In the present
work, we explore the feasibility and the possible advantages
of a MOT using the 2 3 S 1 →3 3 P 2 transition at 389 nm for
metastable helium, in comparison with the conventional
2 3 S 1 →2 3 P 2 共1083-nm兲 magneto-optical trap.
Although the 389-nm transition was used recently in laser
cooling experiments 关6兴, it has not found wide application
yet. This mainly relates to the fact that 10% of the 3 3 P 2
population decays via the 3 3 S 1 state 共Fig. 1兲, making a
closed laser cooling transition between magnetic substates
impossible. In addition, the shorter 389-nm wavelength
leads, in combination with a linewidth ⌫/2␲ ⫽1.5 MHz 关7兴,
to a relatively high saturation intensity I 0 ⫽3.31 mW/cm2
共circular polarization in an optically pumped environment
关8兴兲. In comparison, the 2 3 S 1 →2 3 P 2 transition at 1083 nm
has almost the same linewidth but a saturation intensity of
only 0.17 mW/cm2 . To maximize the number of trapped atoms, dedicated metastable helium magneto-optical traps are
*Electronic address: koel@nat.vu.nl
1050-2947/2003/67共5兲/053406共11兲/$20.00
operated at large detuning and intensity 关5,9,10兴. This implies the need for a high-power laser setup. Nevertheless, the
concept of a 389-nm magneto-optical trap is appealing. An
interesting feature of the 389-nm transition is the momentum
transfer per photon, which is 2.8 times larger than for the
1083-nm photons. Since both transitions have nearly equal
linewidths, the spontaneous cooling force increases proportional to the photon momentum. This opens the possibility to
compress the cloud substantially in comparison to a 1083-nm
MOT at the same detuning and power. Unfortunately, compression may lead to increased losses predominantly due to
light-assisted two-body collisions. The two-body loss rate
coefficient for the 389-nm situation is, however, unknown. In
FIG. 1. Helium level scheme. The long-lived 2 3 S 1 metastable
state is populated in a dc discharge. The 2 3 S 1 →3 3 P 2 共389 nm兲
and 2 3 S 1 →2 3 P 2 共1083 nm兲 laser cooling transitions are indicated
with bold arrows.
67 053406-1
©2003 The American Physical Society
PHYSICAL REVIEW A 67, 053406 共2003兲
KOELEMEIJ et al.
the case of a relatively low rate coefficient, the cloud may be
compressed without loss of too many metastables. Furthermore, it should be noted that the 1083-nm and 389-nm transitions are electronically alike, which greatly facilitates the
comparison between the two MOT types. Finally, the
389-nm MOT differs from the 1083-nm MOT in yet another
respect: two 389-nm photons contain sufficient energy to
ionize an atom in the 2 3 S 1 state. This may introduce observable additional losses.
In this paper, we report on the study of a prototype
389-nm MOT. In Sec. II we present some preliminary considerations regarding laser cooling and trapping at 389 nm.
Next, we outline our experimental setup in Sec. III. Results
are given in Sec. IV. Conclusive remarks and an outlook are
presented in Sec. V.
same assumptions for the MOT parameters, the spring con2
stant ␬ ⫽m ␻ osc
is increased by a factor 2.8. This has implications for the size of the trapped cloud, which is determined
by the equipartition of the potential and kinetic energies. The
volume V of the cloud is 共following the definition of V as
given in Sec. III C 2兲
V⫽
The large photon momentum transfer modifies the equilibrium conditions in a 389-nm MOT with respect to the
1083-nm situation. This follows from regarding the motion
of an atom, trapped in a one-dimensional MOT, as an overdamped harmonic oscillation 关11,12兴. Within this picture, the
oscillation frequency ␻ osc and damping coefficient ⑀ d , for
small velocities and small deviations from trap center, are
given by
4␦S␨
m 共 1⫹2S⫹4 ␦ 2 兲 2
4␦S
m 共 1⫹2S⫹4 ␦ 2 兲 2
,
共3兲
B. Loading the MOT
A. 389-nm MOT versus 1083-nm MOT
⑀ d⫽4បk 2
冊
3/2
where, for simplicity we have assumed an isotropic threedimensional 共3D兲 harmonic oscillator (k B is Boltzmann’s
constant兲. It follows that the volume decreases by a factor
4.5, i.e., the cloud is compressed with respect to the 1083-nm
situation.
II. THEORY
2
␻ osc
⫽4បk
冉
2 ␲ k BT
␬
,
,
共1兲
共2兲
with k being the wave number of the MOT laser light, m
being the atomic mass, ␦ ⫽2 ␲ ⌬/⌫ with ⌬ the laser detuning
from resonance in megahertz, S⫽I/I 0 the saturation parameter, with I being the intensity per MOT beam, and ␨ representing the spatial derivative of the position-dependent Zeeman detuning. The theoretical framework in which Eqs. 共1兲
and 共2兲 are derived assumes that the Doppler shift ⌬ r , corresponding to the recoil velocity, is small compared to the
linewidth ⌫. In the 389-nm case, however, ⌬ r /⌫⫽0.43,
which invalidates the assumption of a small recoil Doppler
shift. Nevertheless, we proceed with our comparison between a 389-nm MOT and a 1083-nm MOT based on Eqs.
共1兲 and 共2兲, assuming that the conclusions will be approximately correct.
The large photon momentum transfer at 389-nm implies
two general differences between the 389-nm and 1083-nm
MOTs, which follow immediately from Eqs. 共1兲 and 共2兲.
First, bearing in mind that k 389⫽k 1083⫻1083/389, it is obvious that for an equal saturation parameter and detuning the
damping coefficient increases by a factor 7.8 as compared to
a 1083-nm MOT. Although this does not alter the temperature in the MOT, which does not depend on wavelength and
is expected to be almost equal for the two cases, the damping
time ␶ is shortened to 0.13␶ 1083 关11兴. Second, and under the
All magnetic substates participate in the atom-laser interaction, since the magneto-optically trapped cloud is contained at low magnetic-field strengths and irradiated from six
directions with circularly polarized light. Therefore, the presence of the second decay channel of the 3 3 P 2 state will not
limit operation of the MOT, as long as there is loading of
atoms from the outer regions of the MOT volume. Loading,
however, may be frustrated by the nonclosed cycling transition as well as by the relatively large Doppler shift. More
specifically, the question arises whether the slowing process
of atoms entering the MOT volume can be completed before
a spontaneous emission via the 3 3 S 1 cascade takes the atom
to a different, nonresonant magnetic substate. If not, the atom
needs to be repumped to the cycling transition; otherwise it
will escape from the MOT volume. To make a conservative
estimate of the capture velocity of a 389-nm MOT, a simple
1D model for an atom traversing the MOT volume is used. In
this model, the MOT is replaced by a 389-nm Zeeman
slower with a length equal to the MOT beam diameter and a
slower laser with detuning equal to the MOT detuning.
We calculate the position-dependent, instantaneous photon scattering rate for atoms at a given velocity v , interacting
with a counterpropagating, red-detuned laser beam at 389 nm
inducing ␴ ⫹ transitions. This laser beam represents the two
MOT laser beams counterpropagating the atomic beam at
angles of ⫾45° with respect to the atomic beam 共see Sec.
III A兲. We assume the atoms to be predecelerated by a Zeeman slower, so that we can choose any initial velocity. We
take Zeeman detuning, laser intensity, and Doppler shift into
account, the latter of which is taken to be k v / 冑2 to correct
for the ⫾45° angle between the atom and 共real兲 laser beams.
Furthermore, we consider all three ␴ ⫹ transitions, i.e., M ⫽
⫺1,0,⫹1→M ⬘ ⫽0,⫹1,⫹2 共of which the M ⫽⫹1→M ⬘ ⫽
⫹2 will be referred to as the laser cooling or cycling transition兲. In Fig. 2, plots are shown of the photon scattering rate
for the three ␴ ⫹ transitions as a function of the distance from
the center of the MOT, measured along the symmetry axis of
the Zeeman decelerator. The MOT light boundaries are at
about ⫾10 mm from the MOT center 共see also Sec. III B兲,
and the atoms are moving into the positive direction. Figure
2共a兲 shows the familiar behavior of the scattering force in a
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PHYSICAL REVIEW A 67, 053406 共2003兲
MAGNETO-OPTICAL TRAP FOR METASTABLE HELIUM . . .
FIG. 2. 共a兲–共c兲 389-nm and 共d兲 1083-nm photon scattering rates
as a function of distance from the MOT center for M ⫽1→M ⬘
⫽2 共solid line兲, M ⫽0→M ⬘ ⫽1 共dashed line兲, and M ⫽⫺1→M ⬘
⫽0 共dash-dotted line兲 transitions.
MOT. An atom, moving into the positive direction at a typical intra-MOT velocity v ⫽1 m/s, scatters an increasing
number of photons from the counterpropagating MOT laser
beam as it moves farther away from the MOT center. Consequently, it will be slowed down and eventually pushed
back toward the center.
First, we use this model to investigate the capture of atoms, emerging from the Zeeman slower in the 2 3 S 1 ,M ⫽
⫹1 state with velocity v ⫽75 m/s. We choose a MOT detuning of ⫺35 MHz, an intensity of 30I 0 , and a magnetic-field
gradient of 20 G/cm. These conditions are typical for a
1083-nm MOT. The model shows that the resonance condition is never fulfilled inside the MOT volume, thus preventing any loading of atoms. Next, we lower v to 35 m/s. We
observe that the atoms now interact strongly with the laser
light within the MOT volume 关see Fig. 2共b兲兴. However, the
peaks in the scattering rate of the different ␴ ⫹ transitions
hardly overlap in space, as a result of their different Zeeman
detunings. Slowing these atoms down to zero velocity requires about 190 absorption-emission cycles, whereas it
takes about 20 cycles 共corresponding to a velocity reduction
of only 4 m/s兲 for the atom to end up in one of the nonabsorbing (M ⫽⫺1 or M ⫽0) states. Consequently, the capture
process is interrupted. Before this M-state atom becomes sufficiently resonant again, such that it is optically pumped back
to the M ⫽⫹1 state, it will have traveled out of resonance
with the cycling transition and can no longer be captured by
the MOT. Only for velocities v ⬍20 m/s, an atom ending up
in the wrong M state is repumped fast enough to continue the
deceleration toward zero velocity 关Fig. 2共c兲兴. From these
simulations, we conclude that the capture velocity of the
389-nm MOT is ⬇24 m/s. This velocity is much smaller
than the ⬃75 m/s capture velocity of a typical 1083-nm
MOT. Figure 2共d兲 illustrates the superior loading capabilities
of a 1083-nm MOT of 15 mm radius. The smaller Doppler
shift allows for faster atoms to be captured, whereas the
closed cycling transition does not impose any constraints on
the magnetic-field strength. In fact, the 1083-nm MOT diameter sets the maximum stopping distance, and thus limits the
capture velocity. Within the picture provided by the model,
increasing the diameter of a 389-nm MOT will not solve the
problem described above. To avoid optical pumping to nonresonant magnetic substates in the outer regions of the MOT,
only small magnetic-field gradients can be tolerated. Then, to
maintain sufficient confinement of the trapped atoms, only
small MOT laser detunings are allowed, thereby limiting the
capture velocity.
We stress that this model is based on crude simplifications
and ignores important features of the MOT. For instance, the
orthogonal MOT laser beams, in combination with the spatially varying, three-dimensional magnetic-field vector, induce ␴ as well as ␲ transitions. Therefore, the conditions
required for repumping to the laser-cooled state may be less
stringent than predicted by our simple model, and we conclude that the capture velocity of a 389-nm MOT will be
somewhat larger than 24 m/s. As will be discussed in Sec.
III A, the relatively low capture velocity has negative consequences for the loading rate, which may be partially overcome by the implementation of an auxiliary Zeeman slower
in the apparatus. In Sec. IV C we present the results of a test
of this auxiliary Zeeman slower concept, as well as a derivation of the 389-nm MOT capture velocity from experimental
data.
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KOELEMEIJ et al.
III. EXPERIMENTAL SETUP
The reduced capture velocity of a 389-nm MOT is a significant limitation, since a helium atomic beam expands dramatically due to transverse heating during Zeeman deceleration 关13兴. Calculations of the rms size of the atomic beam
along the slowing trajectory show an increase in the rms
atomic beam diameter by a factor 1.7 when tuning the end
velocity from 75 m/s down to 25 m/s. This may lead to a
decrease of a factor 3 in metastable flux. In conjunction with
the limited MOT volume, this inevitably will result in a reduced loading rate. To minimize atomic beam expansion at
the end of the Zeeman slower, we overlap the Zeeman slower
laser beam with an additional 1083-nm beam, with identical
circular polarization and similar intensity, but different detuning (⌬⫽⫺80 MHz) obtained using a second AOM. By
choosing the same sign of the quadrupole magnetic-field gradient along the Zeeman slower axis as that of the Zeeman
slower itself, an auxiliary Zeeman slowing stage only centimeters upstream of the MOT volume is established. This
should allow trapping of atoms with velocities up to 75 m/s
at the end of the Zeeman slower. A calculation of the atomic
beam diameter for this case indicates that the loading rate
may be increased by a factor 2.4 compared to the case where
the Zeeman slower decelerates atoms to a velocity of 24 m/s.
A. Vacuum apparatus and production of slow metastables
B. 389 nm laser setup
The first stage in our atomic beam apparatus involves a
liquid nitrogen cooled He* dc discharge source, producing
an atomic beam that is laser collimated using the curvedwave-front technique. The beam source is a copy of the
source described by Rooijakkers et al. 关14兴. The collimated
beam enters a differentially pumped two-part Zeeman slower
that reduces the longitudinal velocity from 1000 m/s to
⬃25 m/s. 1083-nm laser light from a commercial 2 W fiber
laser 共measured bandwidth 8 MHz兲 is used for slowing and
collimation. The laser is stabilized to the 2 3 S 1 →2 3 P 2 transition using saturated absorption spectroscopy in an rfdischarge cell. The ⫺250 MHz detuning for Zeeman slowing is obtained using an acousto-optical modulator 共AOM兲.
Downstream the Zeeman slower, the MOT vacuum chamber
is located, with 20-mm-diameter laser windows for the MOT
beams 共see Fig. 3兲. Two channeltron electron multipliers are
mounted inside to separately detect ions and metastables.
Both channeltrons are operated with negative high voltage at
the front end; however, one of them is put more closely to
the cloud, thereby attracting all positively charged particles
and leaving only the neutral metastables to be detected by
the other. Also, the detector of metastables is hidden behind
an aperture in the wall of the vacuum chamber 共Fig. 3兲,
which provides additional shielding of its electric field. Two
50-A coils, wound around the vacuum chamber and consisting of 17 turns copper tubing each, produce a quadrupole
magnetic field with a gradient of 43 G/cm along the symmetry axis. The field of the second part of the Zeeman slower
inside the MOT region is counteracted with a compensation
coil, mounted at the position of the Zeeman slower exit. The
pressure in the MOT chamber is 2⫻10⫺9 mbars, and increases to 1⫻10⫺8 mbars when the He* beam is switched
on.
The MOT laser light is obtained by frequency doubling
the output of a Coherent 899 titanium:sapphire 共Ti:sapphire兲
laser 共778 nm with few-hundred kilohertz bandwidth兲 in an
enhancement cavity containing a 10 mm Brewster-cut
lithium triborate 共LBO兲 crystal. The cavity length is locked
to the fundamental wavelength using the Hänsch-Couillaud
scheme. The Ti:sapphire laser is pumped by 10 W at 532 nm
from a Spectra-Physics Millennia X laser. We routinely produce 700 mW of 389-nm light; peak values of over 1 W of
389-nm at 2.1 W fundamental power have been achieved.
We measured 4% short-term (⬃10 ms) power fluctuations in
the 389-nm output 关15兴. The LBO crystal is flushed with
oxygen, which increases the output power by about 10%. A
small portion of the UV output is used to stabilize the wavelength to the 2 3 S 1 →3 3 P 2 transition with saturated absorption spectroscopy, while Zeeman tuning the Lamb dip allows
continuous adjustment of the detuning between 0 and
⫾230 MHz. A combination of cylindrical and spherical
lenses transforms the UV beam into a round, parallel, and
approximately Gaussian beam with an 8 mm waist. The
beam profile is truncated by a 20-mm circular aperture, followed by a series of nonpolarizing beam splitters that split
the UV beam into four beams. The individual beam intensities are chosen such that two beams in the horizontal plane
can be retrorefelected, while the intensity of the two vertical
beams along the symmetry axis of the quadrupole field ensures a more or less spherical He* cloud.
FIG. 3. Top view of the MOT vacuum chamber. Not shown are
the vertical MOT laser beams. Dimensions are given in millimeters.
C. MOT diagnostics
1. Time-of-flight measurement
The internal energy of helium metastables can be exploited in measuring time-of-flight 共TOF兲 spectra of a MOT.
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MAGNETO-OPTICAL TRAP FOR METASTABLE HELIUM . . .
PHYSICAL REVIEW A 67, 053406 共2003兲
Electron multipliers directly detect a part of the expanding
cloud after the atoms in the MOT have been released by
suddenly switching off the MOT laser, the magnetic coils,
and the slower beams. The integrated TOF signal as obtained
in such an experiment is proportional to the total number of
trapped atoms, while fitting the recorded signal to a
Maxwell-Boltzmann TOF distribution function gives the
temperature of the cloud. In our experiment, operating the
channeltrons in current mode indeed yields TOF distribution
signals. However, the channeltron gain varies with the rate of
incident metastable atoms and fitting a Maxwell-Boltzmann
distribution function to the TOF data becomes problematic,
as well as the determination of the number of detected atoms
during the TOF. Therefore, we prefer to use the channeltrons
in pulse counting mode: using a properly set amplifier/ discriminator, the count rate is not dependent on the momentary
gain of the channeltron. The output of the amplifier/ discriminator is subsequently integrated by a calibrated ratemeter. The thus obtained TOF distributions purely reflect the
rate of detected metastables and can be used for fit purposes.
The integrated TOF signal gives the number of detected atoms, whereas a Maxwell-Boltzmann fit to the data, which
also takes the response time of the ratemeter into account,
reveals the temperature. Knowing the solid angle covered by
the detection area, the accuracy in the absolute number of
trapped atoms is now determined by the detection efficiency
of a low-velocity triplet helium atom, which is estimated to
be in the range 10–70 % 共see also Refs. 关5,14兴, and references therein兲. This measuring method therefore cannot provide better than 50% accuracy in the absolute number of
trapped atoms.
environment, and I is the laser intensity of a single MOT
beam. The phenomenological factor C incorporates the effects of reduced saturation; as the six circularly polarized
MOT laser beams traverse the cloud in different directions
and at varying angles with the quadrupole magnetic field, all
transitions between the ground- and excited-state Zeeman
levels must be considered, and the saturation intensity I 0 , as
defined above, no longer applies. It is pointed out in Ref.
关16兴 that C lies somewhere halfway the average of the
squared Clebsch-Gordan coefficients of all involved transitions, and 1. For the 2 3 S 1 →3 3 P 2 389-nm transition, the
average of the squares of the Clebsch-Gordan coefficients is
0.56. Therefore, we adopt C⫽0.8⫾0.2, as also chosen by
Browaeys et al. 关9兴. This value incorporates a realistic estimate and an uncertainty that covers the range of all physically possible values of C.
The fluorescence image of the cloud is also used to determine the volume of the cloud. From a fit to a Gaussian distribution, we obtain the rms size in the radial ( ␴ ␳ ) and axial
( ␴ z ) directions, and the volume V⫽(2 ␲ ) 3/2␴ ␳2 ␴ z (V contains 68% of the atoms兲. For a cloud with Gaussian density
distribution, this definition of V conveniently connects the
number of atoms, N, to the central density n 0 via N⫽n 0 V.
This provides all necessary information to deduce the density
distribution n(r).
2. Fluorescence detection
In addition to the determination of the MOT atom number
by time-of-flight measurements, we monitor the fluorescence
of the cloud using a calibrated charge coupled device 共CCD兲
camera to independently determine the number of atoms.
Here, the cascade via the 3 3 S 1 state offers the 707 nm wavelength, which is far more efficiently detected by a camera
than fluorescence from a 1083-nm MOT. Moreover, the 707
nm light does not suffer from reabsorption, because of the
insignificant population of the 2 3 P 2 level. Therefore, we can
safely assume the monitored fluorescence to be proportional
to the number of atoms at each point in the cloud image,
even at the highest densities obtained in our MOT. To calibrate the camera, we use a small fraction of the Ti:sapphire
laser output, with the laser tuned to 707 nm. In the atom
number determination, we use dichroic mirrors to block all
other wavelengths scattered from the MOT, most importantly
the abundant 389-nm light. To extract the number of atoms,
N, from the observed fluorescence power P fluor , we use the
empirical equation of Townsend et al. 关16兴, which relates the
emitted power to the number of atoms:
P fluor⫽Nប ␻
⌫
6CS
.
2 1⫹6CS⫹4 ␦ 2
共4兲
In the above equation, S⫽I/I 0 , where I 0 is the saturation
intensity in the case of ␴ ⫹ transitions in an optically pumped
3. Ion detection
In the MOT vacuum chamber, positive ions are produced
in Penning-ionizing collisions of a He* atom with another
He* atom or with a background-gas molecule. These ions are
subsequently attracted to and detected by the second channeltron, and the resulting output current provides a rough
measure of the number of trapped atoms. This signal is particularly useful for optimization purposes. Moreover, the signal is used to monitor the trap decay after the loading of the
MOT has suddenly been stopped 共see Sec. IV B兲. This channeltron is operated at a sufficiently low voltage, such that the
output current can safely be assumed to vary linearly with
the detection rate.
IV. RESULTS AND DISCUSSION
A. MOT results
1. Temporal fluctuations in the MOT
While observing the fluorescing cloud in real time with
the CCD camera, we noticed nonperiodic intensity fluctuations on a 50 ms time scale. Also, the cloud was irregularly
‘‘breathing.’’ To determine the source of these fluctuations,
we first took a series of ten pictures of the cloud. The shutter
time for each picture was 1/60 s, and the elapsed time between two subsequent exposures was about 5 s. Fitting the
cloud size for each individual picture, we obtain an average
MOT volume with a standard deviation of 9%, while the
temperature remained constant within 2.5%. According to
Eqs. 共1兲 and 共3兲, this may be related to the unstable laser
power. In that case the resulting density fluctuations should
influence the rate at which ions are produced in two-body
Penning collisions. To observe this, we compared the con-
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KOELEMEIJ et al.
tinuous ion signal with the laser intensity as a function of
time. It turns out that the 4% laser intensity noise correlates
to the ion signal noise, though it does not explain all irregularities in the ion signal. Using Eq. 共3兲 we find that the measured intensity fluctuations may give rise to 6% variations in
the deduced MOT volume.
2. Atom number and density distribution
The maximum number of loaded atoms as derived from
the fluorescence is 2.5(3)⫻107 at a detuning ⌬⫽
⫺41 MHz and gradient ⳵ B/ ⳵ z⫽39 G/cm. The total intensity in this case is about 100I 0 . It is possible to run the MOT
at intensities as low as 40I 0 , although the number of trapped
atoms increases with intensity. To ensure a reliable estimate
of the cloud dimensions and fluorescence intensity, we take
the average of five subsequent images. The uncertainty in the
number of trapped atoms mainly arises from the inaccuracy
of the value of the phenomenological constant C 共8%兲, as
well as from an error in the fluorescence measurement. The
uncertainty in the fluorescence measurement is set by the 4%
inaccuracy in the calibration and by the shot-to-shot fluctuations between the individual images used in the average. To
ensure consistency between the results of the fluorescence
and TOF measurement, we have to assign a value of 15共2兲%
to the detection efficiency of the channeltron. A Gaussian
density function fits well to the cloud image. From the fit we
infer the rms radii in the z and ␳ dimensions and, thus, the
volume V. At an optimized trapped atom number, we find
V⫽0.020(5) cm3 . By increasing the magnetic-field gradient
to ⳵ B/ ⳵ z⫽45 G/cm, and decreasing the detuning to ⌬⫽
⫺33 MHz,
the cloud was compressed to V
⫽0.0043(4) cm3 . Still, it contained 1.7(2)⫻107 atoms.
Compared to a 1083-nm MOT, typical values for the volume V of the 389-nm MOT are found to be 6 –25 times
smaller 关5兴. Although the auxiliary laser beam at 1083-nm
acts as a seventh MOT beam, its effect on the cloud volume
is negligible on account of its large detuning 共80 MHz兲, and
the relatively small photon momentum of the 1083-nm light.
Using Eqs. 共1兲 and 共3兲, V can be corrected for the different
magnetic-field gradients, saturation parameters, and temperatures for the 389-nm and 1083-nm cases. It follows that the
observed compression of the cloud, due to only the increased
laser cooling force, is approximately a factor 5, as predicted
in Sec. II A. The optimum number of atoms is achieved with
a relatively large magnetic-field gradient, about twice as
large as in a 1083-nm MOT.
With the knowledge of N and V we can determine the
central density n 0 ⫽N/V, which is 1.4(5)⫻109 cm⫺3 in the
case of optimized trapped atom number. The large error bar,
indicating the spread about the mean of the central densities
obtained from each picture, is probably due to the correlation
between the volume and the 389-nm laser power fluctuations. A sudden increase in power leads to a smaller volume,
while the fluorescence intensity increases, resulting in an
overestimate of the trapped atom number. The aspect ratio
␴ z / ␴ ␳ of the cloud turns out to be 0.96共2兲. We compared this
with the aspect ratio as predicted by Eq. 共1兲: since at equilibrium k BT⫽ ␬ ␳ 具 ␳ 2 典 ⫽ ␬ z 具 z 2 典 , with ␬ ␳ and ␬ z the spring
constants of the MOT in the radial and axial directions, re-
FIG. 4. Two typical TOF spectra 共solid curves兲 and corresponding fits to the data 共dashed curves兲, at detunings ⌬⫽⫺35 MHz and
⌬⫽⫺28 MHz, respectively. The nonzero offset at t⭐0 ms is ascribed to the loss of metastables during loading of the MOT, due to
imperfect alignment.
spectively, it follows that 冑␬ ␳ / ␬ z ⫽ ␴ z / ␴ ␳ , resulting in an
aspect ratio of 0.79. This may indicate a small temperature
difference between the ␳ and z directions, also observed in a
1083-nm MOT 关5兴.
3. Temperature
Fitting a Maxwell-Boltzmann distribution function to the
TOF spectra reveals the temperature T of the atoms in the
MOT 共Fig. 4兲. The fit is not perfect and the deduced temperature may be somewhat overestimated. Furthermore, a
nonzero offset at t⭐0 is observed, which becomes more
prominent 共at the expense of trapped metastables兲 when the
MOT laser beams are misaligned. The offset may also incorporate the loss of metastables due to radiative escape 关1兴, but
our setup does not allow us to discriminate between different
sources of hot metastables. Measured temperatures range
from 0.93共3兲 mK, for ⌬⫽⫺41 MHz and S⫽19, to 0.47共2兲
mK at ⌬⫽⫺9 MHz and S⫽15. In the latter case, however,
the number of atoms in the MOT is limited to only 2.2
⫻105 . These temperatures appear to be somewhat lower
than previously reported temperatures obtained with
1083-nm MOTs, operated under similar conditions
关5,9,10,17–19兴. To illustrate this, we start out from the general observation that 1083-nm MOT temperatures lie slightly
above the prediction by the Doppler cooling theory, which is
given by 关11兴
k BT⫽⫺
ប⌫ 1⫹2NS⫹ 共 2 ␦ 兲 2
.
4
2␦
共5兲
Here, N is the dimensionality of the molasses. When using
Eq. 共5兲 to calculate the 389-nm molasses temperature in order to test our results, two features that distinguish the 389nm transition from the 1083-nm transition are relevant. First,
the transition strength, determined by the Einstein coefficient
A 389⬅⌫ 389⫽2 ␲ ⫻1.5 MHz, is slightly less than for the
1083-nm transition (⌫ 1083⫽2 ␲ ⫻1.6 MHz) 关7兴. This decreases the 389-nm molasses temperature by 8% 共here ⌫ 389
should not be confused with the inverse lifetime: (⌫ 389) ⫺1
⫽106 ns, whereas the lifetime of the 3 3 P state is 95 ns due
to the presence of the extra 3 3 P→3 3 S decay channel 关7兴兲.
053406-6
PHYSICAL REVIEW A 67, 053406 共2003兲
MAGNETO-OPTICAL TRAP FOR METASTABLE HELIUM . . .
Second, the 10% decay via the 3 3 S 1 cascade slightly reduces
the diffusion, as the recoil of the photons involved is randomly distributed. A recalculation of the momentum diffusion constant for this case yields a 3% reduction. Thus, we
expect the 389-nm molasses temperature to be 11% lower
with respect to the 1083-nm case. The predicted temperatures now become 1.0 mK for ⌬⫽⫺41 MHz and S⫽19,
and 0.38 mK for ⌬⫽⫺9 MHz and S⫽15. Comparing these
values with the measured temperatures given above, we find
that for detunings larger than ⬃25 MHz the measured values
lie slightly below the theoretical values, in contrast to what is
found in most 1083-nm MOTs. For smaller detunings, this
situation inverts and the measured temperatures tend to exceed the prediction of the properly modified Eq. 共5兲. This
behavior might indicate that at large detuning sub-Doppler
mechanisms are more efficient than at small detuning. In the
case of smaller detunings, however, the use of Eq. 共5兲 becomes questionable: the large 389-nm photon recoil sets the
recoil-temperature limit to 32 ␮ K, just below the Doppler
limit of 36 ␮ K.
FIG. 5. Lower curve: typical nonexponential decay of the ion
signal after the loading has been stopped at t⫽0 ms. Upper curve:
ion signal obtained after averaging over ten decay curves.
1. Collisional losses
The decay of the MOT is observed by recording the current ␾ (t) from the ion-detecting channeltron 关5,20兴:
冉
B. Trap losses
␾ 共 t 兲 ⫽V ⑀ a ␣ n 0 共 t 兲 ⫹
The number of atoms, N, in the MOT is governed by the
well-known rate equation
dN 共 t 兲
⫽L⫺ ␣ N 共 t 兲 ⫺ ␤
dt
冕
n 共 r,t 兲 d r,
2
3
共6兲
where L denotes the loading rate, and ␣ and ␤ are the loss
rate coefficients for processes involving one and two metastables, respectively. Accordingly, when the loading is interrupted, the local density n changes in time following
dn
⫽⫺ ␣ n⫺ ␤ n 2 .
dt
共7兲
Assuming a Gaussian density profile characterized by a timeindependent width, the losses can be expressed in terms of
the central density n 0 关20兴:
␤ 2
dn 0 共 t 兲
n 0共 t 兲 .
⫽⫺ ␣ n 0 共 t 兲 ⫺
dt
2 冑2
共8兲
The losses are largely due to Penning-ionizing collisions,
which yield one positively charged ion per loss event. These
ions are attracted toward the ion detector, resulting in an ion
flux ␾ .
The loss rate constants are determined from the trap decay
when the loading is stopped by simultaneously blocking all
1083-nm laser beams entering the apparatus. This disables
the Zeeman slower and collimation section, and prevents the
auxiliary Zeeman slower laser beam from contributing to the
two-body collision rate via light-assisted collisions. Switching off the collimation minimizes the Penning ionization
contribution of metastables from the atomic beam and, thus,
reduces the background signal.
⑀ b␤
4 冑2
冊
n 20 共 t 兲 ⫹B.
共9兲
Here, B is a constant background signal and ⑀ a and ⑀ b are the
efficiencies with which ions are produced and detected for
losses due to background and two-body collisions, respectively. Collisions that do not lead to Penning ionization but
do result in trap loss, e.g., collisions with ground-state helium atoms, reduce ⑀ a . Radiative escape may affect ⑀ b . For
the fit procedure, the ratio ⑀ ⫽ ⑀ b / ⑀ a must be known. From
the increase in background pressure when the helium atomic
beam is running, we deduce that the background gas consists
for 80% of helium when the MOT is on. Unfortunately, our
setup is not suited for experimental determination of ⑀ , as
done by Bardou et al. 关20兴. They experimentally found ⑀
⫽4⫾1. Since in our case the background gas involves
mainly ground-state helium atoms, we expect ⑀ a to be
smaller than unity. The value of ⑀ b is probably close to unity:
following Tol et al. 关5兴, one finds that for the 1083-nm case
⑀ b ⬇0.98. We take the obvious underestimate ⑀ ⫽1, which
implies that the result of the fit for ␤ n 0 has to be considered
an upper limit. The result for ␣ can also be obtained by
fitting the tail of the decaying ion signal, where the density is
low enough to neglect the contribution of the two-body
losses. In this way, the significance of ⑀ in the determination
of ␣ is strongly 共but not completely兲 reduced.
A typical example of a decaying ion signal is depicted in
Fig. 5. The decay clearly shows nonexponential behavior,
indicating that two-body collisions contribute significantly to
the total losses. Since laser power fluctuations cause density
fluctuations, much noise is visible in the ion signal. Therefore, an average of ten decay transients is fitted, as also
shown in Fig. 5. Unfortunately, this may affect the reliability
of the fitted parameters as the two-body loss rate depends
nonlinearly on intensity. However, apart from intensity noise,
the 389-nm output remained constant over a period sufficiently long to perform the measurements.
053406-7
PHYSICAL REVIEW A 67, 053406 共2003兲
KOELEMEIJ et al.
The fit procedure yields values for the exponential time
constant ␣ and the nonexponential time constant ␤ n 0 . We
typically find ␣ ⫽2 s⫺1 and ␤ n 0 ⫽3 s⫺1 . This gives the rate
coefficient ␤ from the fit parameter ␤ n 0 , using n 0 from the
␤ ⫽1.0(4)
fluorescence
measurement.
We
find
⫻10⫺9 cm3 /s, at a detuning of ⫺35 MHz. Assuming a
value ⑀ ⫽4, the result becomes ␤ ⫽6(2)⫻10⫺10 cm3 /s. The
value ␤ ⫽1.0(4)⫻10⫺9 cm3 /s, which we interpret as the upper limit, is significantly below the value for the 1083-nm
case of 5.3(9)⫻10⫺9 cm3 /s, reported by Tol et al. 关5兴 using
the same detuning and similar saturation.
The small value for ␤ may be explained by a simple
argument from cold-collision theory. A light-assisted collision can be regarded as two 2 3 S 1 atoms that are resonantly
excited to a molecular complex. For small detunings, this
occurs at a relatively large internuclear separation, where the
molecular potential U is well approximated by the dipoledipole interaction
U ⫾ ⫽⫾
C3
R3
共10兲
.
Here, R is the internuclear distance and C 3 ⯝ប⌫(␭/2␲ ) 3 关1兴.
The excitation by the red-detuned MOT laser light takes
place resonantly when the molecular potential energy compensates the detuning. This sets the so-called Condon radius
RC :
R C⫽
冉
C3
2␲ប兩⌬兩
冊
1/3
.
共11兲
The red detuning selects an attractive molecular state. Once
excited, the two atoms are accelerated toward small internuclear distances, where Penning ionization occurs with high
probability. It follows from Eqs. 共10兲 and 共11兲 that the Condon radius for 389-nm excitation is 2.8 times smaller than for
1083 nm. Classically, the cross section for the collision is
determined by the square of the Condon radius, and is therefore expected to decrease by almost a factor 8.
To identify the role played by light-assisted collisions in
the total two-body losses, we assume that ␤ , as defined in
Eq. 共7兲, can be decomposed in two terms: ␤ SS and ␤ SP . Here
␤ SS is the rate coefficient for losses due to collisions between
2 3 S 1 atoms in the absence of light, whereas ␤ SP takes the
light-assisted collisional losses into account and depends 共for
a given detuning and saturation parameter兲 on the cross section and, thus, on the Condon radius as described above. We
neglect collisions between excited-state atoms, since the
excited-state population in our far-red-detuned MOT does
not exceed 0.01. We can define ␤ SS and ␤ SP also via Eq. 共7兲,
with the total density n replaced by the 2 3 S 1 density n S :
dn S
⫽⫺ ␣ n S⫺ 共 ␤ SS⫹ ␤ SP兲 n S2.
dt
共12兲
Since the excited-state population is small, n S⬇n. It now
follows immediately from Eqs. 共7兲 and 共12兲 that, to good
approximation ␤ ⫽ ␤ SS⫹ ␤ SP .
␤ SS has been measured in a 1083-nm MOT by Tol et al.
SS
⫽2.6(4)⫻10⫺10 cm3 /s. Subtracting this from
关5兴 to be ␤ 1083
the total rate coefficient ␤ 1083⫽5.3(9)⫻10⫺9 cm3 /s, we inSP
⫽5(1)⫻10⫺9 cm3 /s, which is much larger than
fer ␤ 1083
SS
␤ 1083 . In contrast, the upper limit we find for ␤ 389 is of the
SS
共since the 1083-nm and
same order of magnitude as ␤ 389
389-nm magneto-optical traps, operated under the same conditions, are assumed to lead to similar populations of the
SS
SS
⫽ ␤ 1083
). To ob2 3 S 1 , M ⫽⫺1,0,1 levels, we can take ␤ 389
SS
SP
tain the upper limit for ␤ 389 , we subtract ␤ 389 from ␤ 389 and
SP
find ␤ 389
⭐7(3)⫻10⫺10 cm3 /s. This is in good agreement
with the prediction following our simple argument. In addition to the upper limit found for ␤ 389 , we can now assign a
SS
⫽2.6(4)⫻10⫺10 cm3 /s. Summarizlower limit equal to ␤ 389
⫺10
ing, we find 2⫻10
cm3 /s⬍ ␤ 389⬍1.0⫻10⫺9 cm3 /s.
2. Two-photon ionization
From the fit to the ion signal decay, we extract the linear
loss rate coefficient ␣ . Unlike the situation in 1083-nm
magneto-optical traps, ␣ is not solely determined by
background-gas collisions, but also by the two-photon ionization rate. We assume that each loss event involves only
one He* atom and ignore photoionization of the molecular
complex formed during a light-assisted collision, as this process enters Eq. 共8兲 via ␤ . Hence the loss rate coefficient can
be written as
␣ ⫽ ␣ bgr⫹ ␣ 2ph ,
共13兲
where ␣ bgr denotes the background-gas collisional rate, and
␣ 2ph accounts for the two-photon ionization loss rate. Two
processes can be thought to cause the ionization: two-photon
ionization of a 2 3 S 1 atom, or photoionization of an atom in
either the 3 3 P 2 or the 3 3 S 1 state. The latter state is populated only during the cascade and has a lifetime of only 35
ns, so its contribution will be negligible. The instantaneous
two-photon ionization probability p inst is, for not too large
detuning ⌬, dependent on intensity S and MOT detuning ⌬
according to
p inst⬀
S2
⌬2
共14兲
.
The photoionization probability p pi of a helium atom in the
3 3 P 2 state is simply proportional to the incident laser intensity and the cross section for photoionization, which varies
only slowly with wavelength 关21兴. Neglecting this wavelength dependence, the probability of photoionization simply
becomes the product of the upper 3 3 P 2 state population and
the ionization probability itself. For the two-step process,
this leads to a dependence on intensity and detuning as
p pi⬀
S 2 共 ⌫/2兲 2
⌬ 2 ⫹ 共 S⫹1 兲共 ⌫/2兲 2
.
共15兲
When ⌬ 2 Ⰷ(S⫹1)(⌫/2) 2 , this dependence takes on a form
similar to Eq. 共14兲. We confirmed this behavior by measuring
␣ 2ph as a function of MOT detuning, as shown in Fig. 6. We
also checked the intensity dependence, as shown in Fig. 7. In
both cases, we determined ␣ bgr by measuring ␣ as a function
053406-8
PHYSICAL REVIEW A 67, 053406 共2003兲
MAGNETO-OPTICAL TRAP FOR METASTABLE HELIUM . . .
FIG. 6. Two-photon loss rate constant ␣ 2ph versus MOT detuning for total saturation parameter I total /I 0 ⫽6S⫽110.
of background pressure, while keeping the detuning and intensity fixed. Assuming a linear variation of ␣ bgr with pressure, against a fixed background ␣ 2ph , a fit to the data points
yields ␣ bgr⬇1.5(1) s⫺1 . Under typical experimental conditions, we find ␣ 2ph⬇0.5 s⫺1 .
Chang et al. calculated photoionization cross sections of
many singlet and triplet states in helium, including the 3 3 S
and 3 3 P states, for various wavelengths 关21兴. Using their
results, we find photoionization rates of about 2 s⫺1 . Since
the fraction of n⫽3 atoms in our MOT is typically below the
1% level, the net loss rate due to the two-step process then
would be one order of magnitude smaller than the measured
value for ␣ 2ph . This suggests that instantaneous two-photon
ionization dominates over the two-step ionization losses.
C. Auxiliary Zeeman slower, loading rate, and MOT
capture velocity
To test the performance of the auxiliary Zeeman slower,
we first optimized the number of atoms in the MOT in the
absence of the extra slowing laser. Then, leaving the MOT
parameters unaltered, we unblock the auxiliary laser beam
and vary the slower laser intensities and Zeeman coil current
iteratively until a new optimum for the number of atoms is
established. Indeed, blocking the additional laser beam again
interrupts the loading, demonstrating that we have tuned the
end velocity of the Zeeman decelerator above the capture
velocity of the MOT. With the auxiliary Zeeman slower on,
the number of atoms is 40% times larger as compared to the
case without the auxiliary Zeeman slower. Making use of Eq.
共6兲, with ␣ , ␤ , and n 0 known from experiment, we calculate
that the auxiliary Zeeman slower enhances the loading rate
by a factor 1.6. Despite this improvement, the loading rate
remains low. By solving Eq. 共6兲, with the measured values
for the loss rate constants and the steady-state number of
atoms as input, we find a loading rate slightly below
108 s⫺1 . Tol et al. 关5兴 state a value of 5⫻109 s⫺1 for their
1083-nm MOT. This difference is explained by the smaller
MOT diameter, the reduced flux of slow atoms from the
Zeeman slower due to atomic beam expansion, and imperfect
collimation due to the relatively large bandwidth of the
1083-nm laser.
From the Zeeman slower settings, it is possible to calculate the end velocity of the atoms and, thus, the capture velocity of the MOT. Therefore, the equations of motion of an
atom subject to the decelerating laser beam are solved. We
take into account the saturation parameter, the laser beam
intensity profile, and the magnetic field 共obtained from a detailed calculation兲. In this way we derive a capture velocity
of 35 m/s 共without using the auxiliary Zeeman slower兲. Apparently, the prediction of a 24-m/s capture velocity by the
model of Sec. II B is an underestimate, and the true capture
velocity lies close to the velocity determined by the resonance condition. Therefore, it is likely that the ␲ and ␴
transitions, caused by MOT laser beams orthogonal to the
quantization axis, occur at rates at least comparable to the
10% decay via the 3 3 S 1 cascade. Apparently, the nonclosed
character of the 389-nm transition plays a minor role, even in
the case of relatively large (⬃40 G) magnetic fields.
We derive from the settings of the Zeeman slower that
atoms with a velocity of at most 75 m/s are further decelerated to a velocity of 35 m/s by the auxiliary Zeeman slower.
This translates to an increase in loading rate by a factor 1.7,
in reasonable agreement with the result of the test described
above.
D. Comparison with 1083-nm MOT
Table I contains MOT results for the 389-nm and
1083-nm cases 关5兴. Both MOTs have similar detuning and
saturation parameters, which optimize both density and
trapped atom number. The smaller number of atoms, N, in
the 389-nm MOT is explained by the small loading rate.
Despite this small number, the central density n 0 is equal to
that of a 1083-nm MOT containing over one order of magnitude more atoms. This is the result of the smaller loss rate
constant ␤ , the larger laser cooling force, and the larger
magnetic-field gradient. The latter not only contributes to the
compression of the cloud, but also reflects the necessity of a
large Zeeman detuning to compensate the larger Doppler
shift of the atoms to be captured from the Zeemandecelerated He* beam. Furthermore, we observe that the
0.5 s⫺1 contribution of two-photon ionization to the losses in
the 389-nm MOT is small compared to the 21 s⫺1 two-body
loss rate in a large 1083-nm MOT.
V. CONCLUSION AND OUTLOOK
FIG. 7. Two-photon loss rate constant versus total saturation
parameter I total /I 0 at detuning ⌬⫽⫺35 MHz.
We have shown that it is possible to build a magnetooptical trap using the 389-nm transition in triplet helium. Our
053406-9
PHYSICAL REVIEW A 67, 053406 共2003兲
KOELEMEIJ et al.
TABLE I. Comparison of the 389-nm MOT with the 1083-nm
MOT described in Ref. 关5兴. The typical results for both MOTs are
obtained under conditions that optimize both density and atom
number. For the 389-nm case, ⑀ ⫽1 is assumed.
MOT wavelength
Detuning ⌬ 共MHz兲
Magnetic field gradient
⳵ B/ ⳵ z 共G/cm兲
Total intensity (I 0 )
Number of atoms N
Loading rate L (s⫺1 )
Central density n 0 (cm⫺3 )
Volume V (cm3 )
Temperature T 共mK兲
Two-body loss rate ␤ n 0 (s⫺1 )
Two-body loss rate constant
␤ (cm3 /s)
Two-photon ionization
Loss rate constant ␣ 2ph (s⫺1 )
389 nm
1083 nm
⫺35
⫺35
41
100
2⫻107
⬍108
4⫻109
0.005
0.85
3
20
90
5⫻108
⬎5⫻109
4⫻109
0.12
1.1
21
1.0(4)⫻10⫺9
5.3(9)⫻10⫺9
0.5
0
shift implies a reduced capture velocity, and the required
Zeeman slower settings then give rise to a smaller flux of
slow metastables. The nonclosed character of the 389-nm
transition, however, does not play an important role in the
capture process, as well as in the other physics involved in
the MOT.
For the near future we plan an ultimate experiment, in a
configuration with a loading rate increased by two orders of
magnitude. To realize this, a 1083-nm MOT with
⬃30-mm-diameter laser beams will be overlapped with a
⬃10-mm-diameter 389-nm MOT. To avoid large two-body
losses in the trapped cloud due to the presence of reddetuned 1083-nm light, a ⬃5-mm-diameter hole has to be
created in the center of the 1083-nm MOT laser beams. This
configuration will benefit from the superior loading capability of the 1083-nm MOT, as well as from the low-loss 389
nm environment containing a dense cloud at relatively low
temperature. Furthermore, we will test the effectiveness of
389-nm molasses on a metastable helium cloud, precooled
by a 1083-nm MOT. This seems promising not only because
of the low temperatures observed already in our 389-nm
MOT, but also because of the reduced resonant absorption
cross section for 389-nm radiation 共which is about eight
times smaller than for 1083-nm radiation兲. This is explained
as follows. In a dedicated 1083-nm molasses experiment (S
Ⰶ1,⌬⬃⌫), starting with a large, dense cloud of helium
metastables, the relative absorption is rather large 关10兴.
Within the cloud, this results in intensity imbalances between
two counterpropagating molasses laser beams, and these imbalances are believed to reduce the effectiveness of the molasses. The reduced absorption cross section at 389 nm implies a reduced intensity imbalance and we, therefore, hope
to obtain lower temperatures in a dedicated 389-nm molasses.
prototype MOT demonstrates that a 389-nm MOT offers the
advantage of a dense, cold cloud of metastable helium atoms,
as compared to a 1083-nm MOT. The relatively large density
is allowed by the reduced two-body loss rate coefficient ␤ ,
whereas the large spontaneous force facilitates substantial
compression of the cloud. Intensity noise on the 389-nm output, however, compromises the measurement accuracy. Together with the high background pressure and the small value
of ␤ , this has complicated an accurate determination of its
value. We conclude that ␤ lies between the experimentally
determined upper limit 1.0⫻10⫺9 cm3 /s, and the two-body
loss rate constant in the absence of light, 2⫻10⫺10 cm3 /s
determined in Ref. 关5兴. Two-photon ionization losses, although present, do not exclude the future possibility of a
389-nm MOT containing large numbers of metastable helium
atoms at high phase-space density. To this end, however, the
loading rate of the MOT must be improved. A bare 389-nm
MOT has limited loading capabilities since the large Doppler
We are indebted to J. Bouma for his contribution to the
design and construction of the setup. We thank P.J.J. Tol and
N. Herschbach for stimulating discussions. The Space Research Organization, Netherlands, 共SRON兲 is gratefully acknowledged for financial support.
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ACKNOWLEDGMENTS
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PHYSICAL REVIEW A 67, 053406 共2003兲
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